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CNV: Assignment 2

In this assignment, you will implement and evaluate a new Topographica model of V1 and V2 to get experience in building and testing models. You will also write a short research proposal to get experience with locating and understanding scholarly neuroscientific and computational literature, and selecting research topics. The goal is to end the course in a good position to start constructing novel and feasible visual cortex models using Topographica.

You are encouraged to work in pairs of your choosing. Just submit one copy of the assignment, listing your partner, and the mark will be allocated equally to each. It is ok to work together just on Part 1 if you prefer; in that case, one of the pair should submit Part 1, listing both partners, and the other should submit only Part 2 plus a list of the two partners.

Part 1: V1/V2 simulation

You should use the copy of Topographica installed in /group/teaching/cnv/topographica. Then:

• Copy /group/teaching/cnv/topographica/asst2.ty to your own directory, e.g. ~/cnv, and launch it:

  mkdir ~/cnv
  cd ~/cnv
  cp /group/teaching/cnv/topographica/asst2.ty .
  ln -s /group/teaching/cnv/topographica/topographica .
  ./topographica -g asst2.ty
  

  
  
• Run this file for about 500 iterations to see what it does. You will want to open Activity and Projection windows and make sure that both are Auto-refreshing, and then step through it for a while. This file specifies a variant of a LISSOM V1 orientation map. Compared to standard LISSOM, this one is simpler in that it has fewer 'forced' changes over time (e.g. no shrinking of the lateral excitatory radius), and instead it uses a homeostatic plasticity mechanism from "Implementation of homeostatic intrinsic plasticity", Jochen Triesch, ICANN 2005, LNCS 3696 pp.65-70. It also uses a smooth sigmoidal activation function, rather than LISSOM's piecewise-linear threshold function. The result should be a simpler starting point, but it will behave somewhat differently from standard LISSOM.
  
  
• Once you are familiar with the behavior, examine asst2.py in your favorite text editor to see how the model is specified, including how the various Sheets and their parameters are specified. Now add a V2 region to this file, based on the existing V1 region, with one set of afferent connections coming from V1 (rather than two coming from LGN ON and LGN OFF), plus lateral excitatory and inhibitory connections.

  To make sure that your V2 basically works, open an Activity plot window and verify that when you present a training input (by pressing Go), it activates in response. Then try training your network for up to 5000 iterations, in small chunks of a few dozen or a few hundred or a thousand iterations. You will probably want to have a Projection window and an Orientation Preference window open as well, and you may want to enable auto-refresh on them so that they get updated after each chunk of training. Then answer the following questions:

  1. How does the organization of "V2" differ from that of V1? In particular, looking at the Afferent Projection to V2, what do the blobs in each ConnectionField represent? Note that the orientation color coding is always done with respect to the retina -- i.e., a neuron colored red in any map responds strongest to horizontal patterns on the retina. What properties of the input are the V2 neurons selective for? How do they differ from V1 neurons in capability? Show example plots from at least iteration 5000 that illustrate what V1 neurons do and what V2 neurons do.
     
     

  2. With the default parameters, V2 is not likely to organize fully; some neurons will have very patchy connections to V1 (indicating high selectivity), while others remain noisy or with wide, broad connections. The map is also not usually smoothly organized. This result is likely to depend on how often and how well the V2 neurons were activated during training. It may be posible to improve this behavior by modifying parameters such as:

     The homeostatic threshold parameters

     The homeostatic mechanism tries to achieve a specified average level mu of neural activity, and to achieve an exponential distribution of activity levels by adjusting a sigmoid's slope and offset. The speed of adjustment is controlled by eta, the initial threshold slope is a_init, and the initial threshold offset is b_init.

     The afferent strength

     The strength parameter of the connection from V1 to V2 will strongly affect how V2 is activated, at least until homeostatic plasticity evens out.

     The lateral excitatory strength

     The strength parameter of the connection LateralExcitatory from V1 to V1 will strongly affect how both V1 and V2 are activated, at least until homeostatic plasticity evens out.

     There are many other potentially important parameters as well, either in V1 or V2 or the connection between them. Focusing on a small number of these, is it possible to get V2 to organize more fully? Discuss the options that you tried and summarize the results and your interpretations of them. Note that there is no need to do any exhaustive parameter search (given that this sort of training takes hours!), just to try out a small number of possible issues and to report what you learned from them.

  3. The input patterns used in this example consist of up to four Gaussian blobs placed and oriented randomly but with a minimum separation between them. Thus there is no opportunity for learning about long-range correlations, and so we don't expect V2 properties to be qualitatively different from V1 neurons. Change the input patterns to something that does have some large scale structure, and try training the network again. For instance, the enforced separation could be eliminated (by changing min_separation to a small number or zero), all patterns could have the same orientation (by e.g. changing "seed=56+i" to "seed=56"), Lines could be used instead of Gaussians, corners or crosses or angles could be used, etc. Report what input pattern type you tried, and analyze how V2 organizes differently in this case. Does V1 organize differently as well? Does V2 achieve results that are qualitatively different from V1?
     
     
  You will need to submit the answers to these questions (preferably as a PDF file including appropriate figures), plus the code for each variant.

Part 2: Research Proposal

Prepare a short (1-2 page) essay discussing recently published peer-reviewed work on models of topographic maps or experimental data relevant to topographic map formation or function, and proposing concrete computational experiments that you could do to build upon that work and answer an important outstanding question. It's important to propose a question that can be answered computationally (to demonstrate that you are aware of how models are used), and also to propose something novel and feasible. Suggestions on how to write such a proposal are in our Proposal guidelines from the Neuroinformatics Research course, although the marking criteria will be significantly less strict in this course because not all of the students are enrolled in a PhD program.

Submission

Your work must be submitted by 10am Monday, 9 April, using the submit command on Informatics DICE machines (type man submit for more details). Your work should be in the form of one plain PDF or ASCII file per problem, named as listed below. ASCII files can be accompanied by PNG images if desired. Late submissions will not be accepted without good reason, and will be penalized according to the standard university policy of 5% penalty per working day or part of a day.

Example of submit command:

submit msc cnv 2 1a.pdf 1a.ty 1b.pdf 1b.ty 1c.pdf 1c.ty 2.pdf

Tips for getting a good mark

Be sure that you provide evidence that you did each part of this assignment. I can only judge what is actually submitted, so you should make sure that the files you submit make it clear that you have done everything, and thought about everything.

Be sure to cite any information that you use that is not from the course material or your own experience. Including such information is encouraged, but it must be properly cited. You can use the CMVC book Bibliography database for citation information for any paper cited in the CMVC text.

Submissions must be in PDF or in plain ASCII text; images can be added separately in .PNG format if necessary. I can be sure to be able to read those formats; others like .doc or .sxw have a certain probability of working properly, but the probability is far from 1.0. Naming the files as I suggest will make my job a lot easier, because I will be able to see exactly what you are submitting for each problem.

Read and follow my list of writing tips.

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